Not sure which comments I am replying to, but thanks for the suggestions. My use of Excel was simply to copy the code that was giving me problems into a separate applications. Sure enough, there was one term that I determined was the culprit. I was doing a parametric model and the results of the second parameter iteration looked out of scale, so I went back to the first iteration and simply copied and pasted the Mathematica code into Excel and the culpit showed up. I also played around with changing the order of integration with no changes.
The imaginary component of the solution is larger than the real part! Since the models are simply volumes and since the integrand does not have any poles, the size of the imaginary component surprised me.
I wanted to plot the integrand, but it is a six-variable function and I simply cannot figure out how to plot it to look for pathological conditions. As for plotting the solution set, I have yet to figure out how to perform a "batch" parametric variation within Mathematica and then collect and plot the results using Mathematica. At this point, I am doing it the hard way and plotting the results in Excel.
I am just getting into learning how to tell NIntegrate what method or strategy to use in performing the integration. The note that often comes up about a pole or oscillations does not seem to hold, though the way NIntegrate samples may be part of the problem.
The "bug" seems to be that the value 11.4 in Mathematica looks like ||.4 in Excel...pretty obvious. It only occurred in one of the instances of the value 11.4 that appeared in the integrand...the others were ok, so I am hard pressed to understand what the underlying bit structure is that was corrupted that turned 11.4 into ||.4.
That's all for now, but if and when I make any headway, I will report back.